Why can't I import a SVG file from Adobe Illustrator or Inkscape?
This is a very common error with a simple solution.
The error:
Just because you saved your file as SVG, it doesn't mean that the information is in vector format, and blender's SVG importer expects vectors (paths) to create curve objects.
Long winded explanation:
Scalable Vector Graphics (SVG) is defined as

a modularized language for describing two-dimensional vector and mixed vector/raster graphics in XML

What that means is that the SVG format can contain three types of graphic objects:
Vector Graphics (made from the 2D representation of paths, points, lines, shapes, fill etc. )
Raster graphics (bitmap images, as pixel information)
Text (using fonts, and XML character data formatting information).
Currently the Blender's SVG importer can only read paths (vectorial graphics). Raster and text information will not be imported.
So how do I import SVG files correctly then?
In this particular case your illustrator/inkscape file is just a bitmap image contained within the SVG file, but is not an object made of paths.
To convert a raster image (pixels) into vectors (paths or curves) it has to be TRACED
In illustrator select your graphic, and form the menu select: Object-&gt;Live_Trace-&gt;Tracing Options. Then trace.

In Inkscape select Path-&gt;Trace_Bitmap (or press ShiftAltB)

Once the image has been properly traced and saved as SVG, the file should import correctly on Blender.

Random tips to deal with SVGs
When exporting from illustrator un-check this box:

On newer versions of there is an option to save as Adobe CEF when saving as SVG. Do not use that, but SVG instead. (see this question)

To import Text.
Text in illustrator doesn't get translated into outline curves automatically when you save as SGV either: You have to select the text and go to Type-&gt;Create Outlines first. Once is converted to paths, it's easy to create a SVG file that blender can deal with.
Filled Paths.
In Illustrator you can have paths that are filled but not closed. Those paths might not translate correctly in blender, so make sure to close your paths in illustrator before exporting.
Scale:
The scale in which the objects where created might not match blender's scene scale (Read this post). Upon importing you may see that there are new curve objects in the outliner but they might not be visible in blender's 3D viewport because they are too small (or sometimes too large). If that's the case you might need to zoom in on the viewport to find your objects, or you might also need change the clip point for the viewport. You can fix scale/visibility issues re-scaling the imported objects or re-scaling your scene.
For more on this topic please read this and this: